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The Stolper–Samuelson theorem is a basic
theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of th ...
in Heckscher–Ohlin
trade Trade involves the transfer of goods and services from one person or entity to another, often in exchange for money. Economists refer to a system or network that allows trade as a market. An early form of trade, barter, saw the direct excha ...
theory. It describes the relationship between relative prices of output and relative
factor Factor, a Latin word meaning "who/which acts", may refer to: Commerce * Factor (agent), a person who acts for, notably a mercantile and colonial agent * Factor (Scotland), a person or firm managing a Scottish estate * Factors of production, suc ...
rewards—specifically,
real wage Real wages are wages adjusted for inflation, or, equivalently, wages in terms of the amount of goods and services that can be bought. This term is used in contrast to nominal wages or unadjusted wages. Because it has been adjusted to account f ...
s and
real Real may refer to: Currencies * Brazilian real (R$) * Central American Republic real * Mexican real * Portuguese real * Spanish real * Spanish colonial real Music Albums * ''Real'' (L'Arc-en-Ciel album) (2000) * ''Real'' (Bright album) (2010) ...
returns to capital. The theorem states that—under specific
economic An economy is an area of the Production (economics), production, Distribution (economics), distribution and trade, as well as Consumption (economics), consumption of Goods (economics), goods and Service (economics), services. In general, it is ...
assumptions (constant returns to scale,
perfect competition In economics, specifically general equilibrium theory, a perfect market, also known as an atomistic market, is defined by several idealizing conditions, collectively called perfect competition, or atomistic competition. In Economic model, theoret ...
, equality of the number of
factors Factor, a Latin word meaning "who/which acts", may refer to: Commerce * Factor (agent), a person who acts for, notably a mercantile and colonial agent * Factor (Scotland), a person or firm managing a Scottish estate * Factors of production, suc ...
to the number of products)—a rise in the
relative price A relative price is the price of a commodity such as a good or service in terms of another; i.e., the ratio of two prices. A relative price may be expressed in terms of a ratio between the prices of any two goods or the ratio between the price o ...
of a good will lead to a rise in the real return to that factor which is used most intensively in the production of the good, and conversely, to a fall in the real return to the other factor.


History

It was derived in 1941 from within the framework of the
Heckscher–Ohlin model The Heckscher–Ohlin model (, H–O model) is a general equilibrium mathematical model of international trade, developed by Eli Heckscher and Bertil Ohlin at the Stockholm School of Economics. It builds on David Ricardo's theory of comparative ad ...
by Wolfgang Stolper and
Paul Samuelson Paul Anthony Samuelson (May 15, 1915 – December 13, 2009) was an American economist who was the first American to win the Nobel Memorial Prize in Economic Sciences. When awarding the prize in 1970, the Swedish Royal Academies stated that he "h ...
, but has subsequently been derived in less restricted models. As a term, it is applied to all cases where the effect is seen.
Ronald W. Jones Ronald Winthrop Jones (July 5, 1931 – September 27, 2022) was an influential international trade economist and retired Xerox Professor of Economics at the University of Rochester. His highly acclaimed book ''Globalization and the Theory of Inp ...
and
José Scheinkman José Alexandre Scheinkman (born January 11, 1948) is a Brazilian economist, currently the Charles and Lynn Zhang Professor of Economics at Columbia University and the Theodore A. Wells '29 Professor of Economics Emeritus at Princeton University. ...
show that under very general conditions the factor returns change with output prices as predicted by the theorem. If considering the change in real returns under increased
international trade International trade is the exchange of capital, goods, and services across international borders or territories because there is a need or want of goods or services. (see: World economy) In most countries, such trade represents a significant ...
a robust finding of the theorem is that returns to the scarce factor will go down,
ceteris paribus ' (also spelled '; () is a Latin phrase, meaning "other things equal"; some other English translations of the phrase are "all other things being equal", "other things held constant", "all else unchanged", and "all else being equal". A statement ...
. An additional robust corollary of the theorem is that a compensation to the scarce factor exists which will overcome this effect and make increased trade
Pareto optimal Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engine ...
. The original
Heckscher–Ohlin model The Heckscher–Ohlin model (, H–O model) is a general equilibrium mathematical model of international trade, developed by Eli Heckscher and Bertil Ohlin at the Stockholm School of Economics. It builds on David Ricardo's theory of comparative ad ...
was a two-factor model with a labor market specified by a single number. Therefore, the early versions of the theorem could make no predictions about the effect on the unskilled labor force in a high-income country under trade liberalization. However, more sophisticated models with multiple classes of worker productivity have been shown to produce the Stolper–Samuelson effect within each class of labor: Unskilled workers producing traded goods in a high-skill country will be worse off as international trade increases, because, relative to the world market in the good they produce, an unskilled
first world The concept of First World originated during the Cold War and comprised countries that were under the influence of the United States and the rest of NATO and opposed the Soviet Union and/or communism during the Cold War. Since the collapse of ...
production-line worker is a less abundant factor of production than capital. The Stolper–Samuelson theorem is closely linked to the factor price equalization theorem, which states that, regardless of international factor mobility, factor prices will tend to equalize across countries that do not differ in technology.


Derivation

Considering a two-good economy that produces only wheat and cloth, with labor and land being the only factors of production, wheat a land-intensive industry and cloth a labor-intensive one, and assuming that the price of each product equals its marginal cost, the theorem can be derived. The price of cloth should be: : (1) P(C)= ar + bw, \, with ''P''(''C'') standing for the price of cloth, ''r'' standing for rent paid to landowners, ''w'' for wage levels and ''a'' and ''b'' respectively standing for the amount of land and labor used, and do not change with the prices of goods. Similarly, the price of wheat would be: : (2) P(W) = cr + dw \, with ''P''(''W'') standing for the price of wheat, ''r'' and ''w'' for rent and wages, and ''c'' and ''d'' for the respective amount of land and labor used, and also considered to be constant. If, then, cloth experiences a rise in its price, at least one of its factors must also become more expensive, for equation 1 to hold true, since the relative amounts of labor and land are not affected by changing prices. It can be assumed that it would be labor—the factor that is intensively used in the production of cloth—that would rise. When wages rise, rent must fall, in order for equation 2 to hold true. But a fall in rent also affects equation 1. For it to still hold true, then, the rise in wages must be more than proportional to the rise in cloth prices. A rise in the price of a product, then, will more than proportionally raise the return to the most intensively used factor, and decrease the return to the less intensively used factor.


Criticism

The validity of the Heckscher–Ohlin model has been questioned since the classical Leontief paradox. Indeed, Feenstra called the Heckscher–Ohlin model "hopelessly inadequate as an explanation for historical and modern trade patterns". As for the Stolper–Samuelson theorem itself, Davis and Mishra recently stated, "It is time to declare Stolper–Samuelson dead". They argue that the Stolper–Samuelson theorem is "dead" because following
trade liberalization Free trade is a trade policy that does not restrict imports or exports. It can also be understood as the free market idea applied to international trade. In government, free trade is predominantly advocated by political parties that hold econ ...
in some developing countries (particularly in Latin America),
wage inequality In economics, income distribution covers how a country's total GDP is distributed amongst its population. Economic theory and economic policy have long seen income and its distribution as a central concern. Unequal distribution of income causes ec ...
rose, and, under the assumption that these countries are labor-abundant, the SS theorem predicts that wage inequality should have fallen. Aside from the declining trend in wage inequality in Latin America that has followed trade liberalization in the longer run (see Lopez-Calva and Lustig), an alternative view would be to recognize that technically the SS theorem predicts a relationship between output prices and relative wages. Papers that compare output prices with changes in relative wages find moderate-to-strong support for the Stolper–Samuelson theorem for
Chile Chile, officially the Republic of Chile, is a country in the western part of South America. It is the southernmost country in the world, and the closest to Antarctica, occupying a long and narrow strip of land between the Andes to the east a ...
,
Mexico Mexico (Spanish: México), officially the United Mexican States, is a country in the southern portion of North America. It is bordered to the north by the United States; to the south and west by the Pacific Ocean; to the southeast by Guatema ...
, and
Brazil Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both South America and Latin America. At and with over 217 million people, Brazil is the world's fifth-largest country by area ...
.


See also

* Wage insurance *
Heckscher–Ohlin model The Heckscher–Ohlin model (, H–O model) is a general equilibrium mathematical model of international trade, developed by Eli Heckscher and Bertil Ohlin at the Stockholm School of Economics. It builds on David Ricardo's theory of comparative ad ...


Further reading

* *


References

{{DEFAULTSORT:Stolper-Samuelson Theorem Economics theorems